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On Rings with Involution

Published online by Cambridge University Press:  20 November 2018

I. N. Herstein
I. N. Herstein*
Affiliation:
University of Chicago, Chicago, Illinois; Weizmann Institute of Science, Rehovot, Israel
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In this note we prove some results which assert that under certain conditions the involution on a prime ring must satisfy a form of positive definiteness. As a consequence of the first of our theorems we obtain a fairly short and simple proof of a recent theorem of Lanski [3]. In fact, in doing so we actually generalize his result in that we need not avoid the presence of 2-torsion. One can easily adapt Lanski's original proof, also, to cover the case in which 2-torsion is present. This result of Lanski has been greatly generalized in a joint work by Susan Montgomery and ourselves [2].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 4 , August 1974 , pp. 794 - 799
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Herstein, I. N., Topics in ring theory (Univ. of Chicago Press, Chicago, 1969).Google Scholar
2. Herstein, I. N. and Susan Montgomery, Invertible and regular elements in rings with involution, J. Algebra 25 (1973), 390–400.Google Scholar
3. Lanski, Charles, Rings with involution whose symmetric elements are regular, Proc. Amer. Math. Soc. 83 (1972), 264–270.Google Scholar
4. Lanski, Charles and Montgomery, S., Lie structure of prime rings of characteristic 2 (to appear).Google Scholar